An ac-dc power distribution network distributed robust state estimation method based on smart meter data

Abstract

The application discloses a kind of AC-DC distribution network distributed robust state estimation method based on intelligent electric meter data, the method utilizes historical state to predict the state interval of current time, and based on nonlinear optimization model is corrected to ensure the rationality of predicted interval;Then, the nonlinear equation scaling method based on mean value theorem is used to convert the nonlinear interval SE model into a linear optimization model, to ensure the completeness of the estimation interval.The algorithm proposed in the application can accurately obtain the interval information of AC-DC distribution network state in weak observable AC-DC distribution network under high proportion of new energy penetration, and provide technical support for subsequent safety evaluation and optimal operation.

Description

TECHNICAL FIELD

[0001] The application provides a method for distributed robust state estimation of AC / DC distribution network based on smart meter data, and belongs to the field of DC power grid distribution. BACKGROUND

[0002] With the vigorous development of renewable energy and the continuous increase of flexible load, the traditional AC distribution network gradually transforms into AC / DC distribution network. As one of the basic functions of energy management system, the state estimation technology can filter out bad data and obtain state variables, thereby providing basic support for subsequent optimal operation and economic dispatch. As one of the basic methods of robust state estimation, the weighted least absolute value (WLAV) can automatically filter out measurement noise and bad data, and ensure high estimation accuracy.

[0003] Unlike the power transmission network which has sufficient measurement information, the measurement data provided by the supervisory control and data acquisition (SCADA) system in the distribution network is very limited, which is difficult to meet the observability requirement. Therefore, the state estimation of the distribution network generally needs to be assisted by pseudo-measurement modeling technology to ensure observability, so as to obtain satisfactory estimation results. At the same time, with the rapid development and wide popularization of smart meters (SM), more useful information is provided for real-time monitoring of the distribution network. In view of this, how to effectively utilize the smart meter data to improve the estimation accuracy and convergence of the state estimation of the distribution network.

[0004] In recent years, many experts and scholars have focused on the research of power flow calculation and state estimation of AC / DC distribution network to ensure safe and economic operation. At present, the research on state estimation of AC / DC distribution network mainly includes two types: centralized state estimation and distributed state estimation. The present application mainly focuses on the distributed state estimation of AC / DC distribution network, that is, the AC system and the DC system are estimated respectively, and only the boundary information is exchanged. At present, the distributed state estimation of AC / DC distribution network mainly adopts the weighted least square method (WLS), which needs to be iteratively calculated for each AC / DC system, exchange the boundary information, and then judge the convergence. This sequential iterative calculation strategy needs to consume a large amount of calculation time, which is not conducive to the promotion in the state estimation of large-scale AC / DC distribution network. Therefore, the present application provides a method for distributed robust state estimation of AC / DC distribution network based on smart meter data, which linearizes the nonlinear AC flow measurement function and establishes a linear robust state estimation. Through regional linear estimation and multi-region parallel calculation, the calculation speed and convergence are greatly improved. SUMMARY

[0005] The application aims at solving the above problems, and provides a robust state estimation method for AC / DC distribution network based on smart meter data, which can accurately obtain real-time state information in the AC / DC distribution network.

[0006] The technical scheme is characterized in that the robust state estimation method for AC / DC distribution network based on smart meter data comprises the following steps:

[0007] Step 1: a three-phase model of the AC / DC distribution network is established according to parameter information of the AC / DC distribution network, wherein the parameter information comprises resistance and reactance of three-phase branches of the AC distribution network, resistance of three-phase branches of the DC distribution network, and equivalent resistance and reactance of the equivalent model of the voltage source converter;

[0008] Step 2: a deep learning model is established, historical smart meter data and sample data generated by power flow calculation are used for offline training, wherein node voltage amplitude data and branch power data in the sample data are input during training of the deep learning model, and node active power injection and node reactive power injection are output during training of the deep learning model;

[0009] Step 3: real-time measurements of node voltage amplitude and branch power are read, and the real-time measurements are input into the trained deep learning model to obtain node active power injection and node reactive power injection pseudo-measurements;

[0010] Step 4: a linear weighted least absolute value estimation model of the AC system is established, and a weighted least absolute value estimation model of the DC system is established;

[0011] Step 5: real-time SCADA measurements, node injection power pseudo-measurements, zero injection constraints and boundary information are brought into the linear weighted least absolute value estimation model of the AC system and the weighted least absolute value estimation model of the DC system established in step 4, and robust estimation is performed on the AC system and the DC system respectively to calculate state estimation values of the AC system and the DC system, wherein the SCADA measurements comprise node voltage amplitude and branch power measurements, the node injection power pseudo-measurements are node active power injection and node reactive power injection generated by the deep learning model in step 3, the zero injection constraints refer to zero active injection and zero reactive injection of tie-in nodes in the power grid, and the boundary information refers to loss power, active power and reactive power of the voltage source converter at the connection boundary of the AC network and the DC network;

[0012] Step 6: boundary information of the AC system and the DC system is calculated based on the state estimation values, the boundary information of the AC system and the DC system is exchanged, and it is judged whether the difference between the boundary information calculated in different regions is within an allowable error range, if not, the boundary information is updated, steps 5 and 6 are repeated, and if yes, the state estimation values of the AC system and the DC system are saved and output.

[0013] Furthermore, in step 1, a three-phase model of the AC / DC distribution network is established based on the parameter information of the AC / DC distribution network. The parameter information includes the resistance and reactance of the three-phase branches of the AC distribution network, the resistance of the three-phase branches of the DC distribution network, and the equivalent resistance and reactance of the voltage source converter equivalent model. The constructed three-phase model of the AC / DC distribution network includes state variables, measurement equations, and a converter equivalent model, as follows:

[0014] (1.1) State variables

[0015] The state variables x of the AC / DC distribution network include the voltage amplitude and phase angle of the AC node and the voltage amplitude of the DC node, as shown below:

[0016]

[0017] Where x AC,i represents the state variable of the ith communication node, x DC,j represents the state variable of the jth DC node, N AC and N DC A collection of nodes representing the AC system and the DC system;

[0018] (1.2) Measurement equations and converter equivalent models

[0019] AC and DC current measurement equations can be expressed as follows:

[0020] zh(x)=e

[0021] Where z represents the measurement vector, x represents the state variable vector, h() represents the AC or DC power flow equation, and e represents the measurement residual vector;

[0022] For AC systems, the measurements include node voltage amplitude measurement, node active injection power measurement, node reactive injection power measurement, branch active power measurement, and branch reactive power measurement. The power flow equation is as follows:

[0023]

[0024]

[0025] θ ii' =θ i -θ i' {i,i'}∈N AC

[0026] Where, P AC,ii’ and Q AC,ii’ Represent the active and reactive powers of the branches connected to the i-th AC node and the i'th AC node, respectively. V i and V i’V ii’ θ i and θ i’ P AC,i and Q AC,i Pi and Qi represent the node active power injection and the node reactive power injection at the ith AC node, respectively, and and and Gi and Gj represent the node active power injection measurement error and the node reactive power injection measurement error at the ith AC node, respectively, ii’ and B ii’ Y i and V i’ , V i and θ i’ belong to the part corresponding to the AC system in the state variable vector x;

[0027] For the DC system, the measurements include the node voltage amplitude measurement, the node active power injection measurement, and the branch active power measurement, and the power flow equation is as follows:

[0028]

[0029] V j and V j’ represent the voltage amplitude of the jth DC node and the j'th DC node, respectively, DC,j Pj represents the active power injection of the jth DC node, DC,jj’ P represents the branch active power of the branch connected between the jth DC node and the j'th DC node, jj’ Y represents the branch admittance of the branch connected between the jth DC node and the j'th DC node, represents the active power injection measurement error of the jth DC node, represents the branch active power measurement error of the branch connected between the jth DC node and the j'th DC node, and V j and V j’ belong to the part corresponding to the DC system in the state variable vector x;

[0030] For the voltage source converter at the boundary of AC / DC system, an equivalent model of the converter is constructed: assuming that a certain converter in the AC / DC distribution network is connected to AC node i, the converter is equivalent to a model connected by an equivalent AC branch and an ideal converter, the two endpoints of the equivalent AC branch are the i th AC node and the equivalent c th AC node, and the measurement equation of the converter is as follows:

[0031] P AC,ci -P VSC =0

[0032] Q AC,ci -Q VSC =0

[0033] P VSC +P VSC,loss =P DC,jc

[0034] In the formula, P VSC represents the active power of the converter, Q VSC represents the reactive power of the converter, P AC,ci and Q AC,ci represent the active power and reactive power flowing from the c th AC node to the i th AC node, P VSC,loss represents the active power loss on the converter, and P DC,jc represents the active power flowing from the j th DC node to the c th AC node.

[0035] Further, the process of establishing, training and applying the deep learning model in step 2 is as follows:

[0036] (2.1) Offline training of deep learning model

[0037] According to the historical smart meter data, learn the distribution of node active injection and reactive injection power, use Monte Carlo sampling to obtain the active injection power and reactive injection power of the node, and calculate the voltage amplitude and phase angle of all nodes in the network through the power flow equation formula in step 1; according to the voltage amplitude and phase angle of all nodes in the network, according to the node position of SCADA measuring point, calculate the corresponding node related branch active power and reactive power according to the power flow formula in step 1, add Gaussian noise to the calculated branch active and reactive power and the corresponding node voltage amplitude to simulate the SCADA measurement value, which is used as the input of the deep learning model, and the expected output of the offline training of the deep learning model is the node active injection power and reactive injection power, the parameters of the deep learning model are adjusted through training samples and test samples until the accuracy meets the requirements;

[0038] (2.2) Online calculation of deep learning model

[0039] According to real-time SCADA measurements, including node voltage amplitude measurements and branch power measurements, they are input into the deep learning model which has been trained, and the output is the node active power and node reactive power at the current time, which is used as the node injection power pseudo measurement.

[0040] Further, step 3 reads the real-time measurements of node voltage amplitude and branch power, which are collected by SCADA measurement devices; the read real-time measurements are input into the trained deep learning model to obtain the node active power and node reactive power at the current time, which are used as the node injection power pseudo measurement.

[0041] Further, the linearized weighted least absolute value estimation model of the alternating current system and the linearized weighted least absolute value estimation model of the direct current system in step 4 are as follows:

[0042] For the AC-DC distribution network, the converter naturally divides into multiple AC and DC systems. For the estimation model of the kth AC region, it is expressed as follows:

[0043]

[0044] s.t.z k -h(x k )=e k

[0045] P AC,ci =P VSC,k ,Q AC,ci =Q VSC,k

[0046] P DC,jc -P VSC,loss =P VSC,k'

[0047] In the formula, J() represents the optimization objective function, x k represents the state variable vector of the kth AC region, λ represents a constant coefficient, P VSC,k and P VSC,k’ represent the converter active power of the kth AC region and the k'th DC region respectively, Q VSC,k is the converter reactive power of the kth AC region, z k represents the measurement vector of the kth AC region, e k represents the measurement residual vector of the kth AC region.

[0048] The linearized expression of the nonlinear power flow equation of the AC system branch power in step 1 is as follows:

[0049]

[0050] wherein U i and U i’ are squares of voltage magnitudes of the ith AC node and the ith' AC node, respectively, R ii’ and X ii’ are resistance and reactance values of branches connected to the ith AC node and the ith' AC node;

[0051] Linearize the nonlinear power flow equation of the AC system in step 1 to obtain the linearized measurement equation:

[0052]

[0053] wherein represents a vector of the node voltage magnitude phasors of the AC system, and H is a constant Jacobian matrix;

[0054] The linearized model of the DC system is:

[0055] P DC,jj' = (1-ΔV j )(1-ΔV j' )Y jj'

[0056] ≈ (1-ΔV j -ΔV j' )Y jj'

[0057] wherein ΔV j and ΔV j’ are differences of voltage magnitudes of the jth DC node and the j' th DC node relative to 1, i.e., V j = 1-ΔV j , V j’ = 1-ΔV j’ ;

[0058] For the kth AC region, the linear weighted least absolute value estimation model is:

[0059]

[0060] s.t.u k -l k = z k -H k x k,AC u k,i , l k,i ≥ 0

[0061] a k -b k = P VSC,k -P VSC,k' a k , b k ≥ 0

[0062] P AC,ci = P VSC,k , Q AC,ci = Q VSC,k

[0063] P DC,jc = P VSC,loss , Q VSC,k' k'∈D k

[0064] where D k represents the set of DC regions connected to the kth AC region, J k represents the optimization objective function of the kth AC region, m k represents the number of measurements in the kth AC region, which is the sum of the number of real-time measurements, the number of pseudo measurements and the number of zero injection constraints in the kth AC region, w k,i represents the weight of the ith measurement in the kth AC region, u k,i -l k,i represents the ith measurement residual of the kth AC region, u k -l k represents the measurement residual vector of the kth AC region, where u k,i and l k,i are non-negative numbers, a k -b k represents the boundary information imbalance of the kth AC region, where a k and b k are non-negative numbers, H k is the constant Jacobian matrix of the kth AC region, x k,AC is the state estimation vector of the kth AC region.

[0065] For the k'th DC region, the linear weighted least absolute value estimation model is:

[0066]

[0067] s.t.u k' -l k' = z k' -H k' x k',DC u k',j , l k',j ≥ 0

[0068] a k' -b k' = P VSC,k -P VSC,k' a k' , b k' ≥ 0

[0069] P AC,ci = P VSC,k Q AC,ci = Q VSC,k

[0070] P DC,jc - P VSC,loss = P VSC,k' k' ∈ D k

[0071] wherein J k’ represents the optimization objective function of the k'th DC area, m k’ represents the number of measurements in the k'th DC area, w k’,j represents the weight of the jth measurement in the k'th DC area, u k’,j - l k’,j represents the jth measurement residual in the k'th DC area, u k ' - l k ' represents the measurement residual vector of the k'th DC area, wherein u k’,j and l k’,j are non-negative numbers, a k’ - b k’ represents the boundary information imbalance of the k'th DC area, wherein a k’ and b k’ are non-negative numbers, H k’ is the constant Jacobian matrix of the k'th DC area, x k’,DC is the state estimation vector of the k'th DC area, and z k’ is the measurement vector of the k'th DC area.

[0072] Further, the boundary information calculation method of step 5 is as follows:

[0073]

[0074]

[0075] P AC,ci = P DC,jc - P VSC,loss

[0076] wherein d1, d2, d3 represent the constant coefficients of the converter loss, V c and I c represent the voltage and current amplitudes of the AC side connection point of the converter.

[0077] Further, the criterion that the boundary information difference is within the allowed error range is as follows:

[0078] PVSC,k -P VSC,k' ≤τ or l < L max

[0079] where τ is a preset convergence threshold, l represents the current iteration number, and L max is the maximum iteration number between areas.

[0080] Beneficial effects: Compared with the prior art, the technical scheme of the present application has the following beneficial technical effects:

[0081] The present application firstly constructs a distributed robust state estimation model of AC-DC distribution network based on smart meter data in view of the characteristics of low measurement redundancy, inconsistent measurement time scale, and prominent three-phase imbalance in AC-DC distribution network. The method uses historical smart meter data and power flow calculation to train the deep learning model of node injection power, so as to generate node injection power pseudo-measurement consistent with the update frequency of SCADA measurement, and construct a distributed robust state estimation model based on SCADA measurement, node injection power pseudo-measurement and equation constraints to ensure the accuracy of the estimation result. Then, the linearization of the AC system converts the complex distributed robust state estimation into a linear robust state estimation model to improve the calculation speed. The algorithm proposed in the present application can quickly obtain accurate state estimation results in the AC-DC distribution network with low measurement redundancy, providing technical support for the safe and economic operation of the subsequent AC-DC distribution network. BRIEF DESCRIPTION OF DRAWINGS

[0082] Figure 1 is a deep learning model of node injection power;

[0083] Figure 2 is a flow chart of the AC-DC distribution network distributed robust state estimation method described in the present application;

[0084] Figure 3 is a test system diagram of AC-DC distribution network;

[0085] Figure 4 is a node 5 and 9 active power injection distribution statistical diagram, (a) node 5 active power probability distribution statistical diagram, (b) node 9 active power probability distribution statistical diagram;

[0086] Figure 5 is a deep learning model output node power error diagram, (a) deep learning model output node active power error diagram, (b) deep learning model output node reactive power error diagram;

[0087] Figure 6 is a comparison diagram of the error of three state estimation methods under different pseudo-measurement models, (a) AC node state estimation error under different pseudo-measurement models, (b) DC node state estimation error under different pseudo-measurement models. DETAILED DESCRIPTION

[0088] The technical solutions of the present application are further described below in combination with the drawings and examples.

[0089] The present application proposes a robust state estimation method for AC / DC distribution network based on smart meter data, comprising the following steps:

[0090] Step 1: Establish a three-phase model of the AC / DC distribution network according to the parameter information of the AC / DC distribution network, wherein the parameter information includes the resistance and reactance of the three-phase branch of the AC distribution network, the resistance of the three-phase branch of the DC distribution network, and the equivalent resistance and reactance of the equivalent model of the voltage source converter.

[0091] Step 2: Establish a deep learning model, use historical smart meter data and power flow calculation to generate sample data, and train offline, wherein the node voltage amplitude data and branch power data in the sample data are input during the training of the deep learning model, and the node active power injection and node reactive power injection are output during the training of the deep learning model.

[0092] Step 3: Read the real-time measurement of node voltage amplitude and branch power, and input the real-time measurement into the trained deep learning model to obtain the node active power injection and node reactive power injection pseudo-measurement.

[0093] Step 4: Establish a linear weighted least absolute value estimation model for the AC system and a weighted least absolute value estimation model for the DC system.

[0094] Step 5: Bring the real-time SCADA measurement, node injection power pseudo-measurement, zero injection constraint, and boundary information into the linear weighted least absolute value estimation model for the AC system and the weighted least absolute value estimation model for the DC system established in step 4, and perform robust estimation on the AC and DC systems respectively to calculate the state estimation values of the AC and DC systems, wherein the SCADA measurement includes node voltage amplitude and branch power measurement, the node injection power pseudo-measurement is the node active power injection and node reactive power injection generated by the deep learning model in step 3, the zero injection constraint means that the active injection and reactive injection of the tie-in node in the power grid are zero, and the boundary information means the loss power, active power, and reactive power of the voltage source converter at the connection boundary of the AC network and the DC network.

[0095] Step 6: Calculate the boundary information of the AC and DC systems based on the state estimation values, exchange the boundary information of the AC and DC systems, and judge whether the difference between the boundary information calculated in different regions is within the allowed error range, if not, update the boundary information and repeat steps 5 and 6; if yes, save and output the state estimation values of the AC and DC systems.

[0096] Further, the step 1 establishes the three-phase model of the AC-DC power distribution network according to the parameter information of the AC-DC power distribution network, and the parameter information includes the resistance and reactance of the three-phase branch of the AC power distribution network, the resistance of the three-phase branch of the DC power distribution network, the equivalent resistance and reactance of the voltage source converter equivalent model, and the established three-phase model of the AC-DC power distribution network includes state variables, measurement equations and converter equivalent models, and specifically as follows:

[0097] (1.1) State variables

[0098] The state variables x of the AC-DC power distribution network include the voltage amplitude and phase angle of the AC node, and the voltage amplitude of the DC node, as shown below:

[0099]

[0100] In the formula, x AC,i represents the state variable of the i-th AC node, x DC,j represents the state variable of the j-th DC node, N AC and N DC represent the node set of the AC system and the DC system;

[0101] (1.2) Measurement equation and converter equivalent model

[0102] The AC and DC measurement equations can be expressed as follows:

[0103] z-h(x)=e

[0104] In the formula, z represents the measurement vector, x represents the state variable vector, h() represents the AC or DC power flow equation, and e represents the measurement residual vector;

[0105] For the AC system, the measurement quantities include node voltage amplitude measurement, node active power injection measurement, node reactive power injection measurement, branch active power measurement and branch reactive power measurement, and the power flow equation is as follows:

[0106]

[0107]

[0108]

[0109] θ ii' =θ i -θ i' {i,i'}∈N AC

[0110] In the formula, P AC,ii’ and Q AC,ii’ represent the branch active and reactive power of the branch connected between the i-th AC node and the i'-th AC node, Vi and V i’ Represent the voltage amplitude of the i-th AC node and the i'th AC node, θ ii’ Represents the phase angle difference between the branches connected to the i-th AC node and the i'th AC node, θ i and θ i’ Represent the phase angles of the ith AC node and the i'th AC node, P AC,i and Q AC,i represent the active injection power and reactive injection power of the i-th AC node, respectively. and represent the branch active power measurement error and branch reactive power measurement error of the branch connected to the i-th AC node and the i'th AC node, respectively. and They represent the measurement error of active power injection and reactive power injection of the i-th AC node, G ii’ and B ii’ Represent the real and imaginary parts of the admittance matrix of the branch connected to the ith AC node and the ith' AC node, respectively. The voltage amplitude V in the AC system power flow equation is i and V i’ , voltage phase angle θ i and θ i’ The part corresponding to the AC system in the state variable vector x;

[0111] For DC systems, measurements include node voltage amplitude measurement, node active injection power measurement, and branch active power measurement. The power flow equation is as follows:

[0112]

[0113] Where V j and V j’ Represent the voltage amplitudes of the jth DC node and the j'th DC node, P DC,j represents the active injection power of the jth DC node, P DC,jj’ represents the branch active power of the branch connected to the jth DC node and the j'th DC node, Y jj’ represents the branch admittance of the branch connecting the jth DC node and the j'th DC node, represents the measurement error of the active injected power at the jth DC node, represents the branch active power measurement error of the branch connected to the jth DC node and the j'th DC node, and the voltage amplitude V in the DC system power flow equation. j and V j’ The part corresponding to the DC system in the state variable vector x;

[0114] For the voltage source converter at the boundary of AC / DC system, an equivalent model of the converter is constructed: assuming that a certain converter in the AC / DC distribution network is connected to AC node i, the converter is equivalent to a model connected by an equivalent AC branch and an ideal converter, the two endpoints of the equivalent AC branch are the i th AC node and the equivalent c th AC node, and the measurement equation of the converter is as follows:

[0115] P AC,ci -P VSC =0

[0116] Q AC,ci -Q VSC =0

[0117] P VSC +P VSC,loss =P DC,jc

[0118] In the formula, P VSC represents the active power of the converter, Q VSC represents the reactive power of the converter, P AC,ci and Q AC,ci represent the active power and reactive power flowing from the c th AC node to the i th AC node, P VSC,loss represents the active power loss of the converter, and P DC,jc represents the active power flowing from the j th DC node to the c th AC node.

[0119] Further, the process of establishing, training and applying the deep learning model in step 2 is as follows:

[0120] (2.1) Offline training of deep learning model

[0121] According to the historical smart meter data, learn the distribution of node active injection and reactive injection power, use Monte Carlo sampling to obtain the active injection power and reactive injection power of the node, and calculate the voltage amplitude and phase angle of all nodes in the network through the power flow equation formula in step 1; according to the voltage amplitude and phase angle of all nodes in the network, according to the node position of SCADA measuring point, according to the power flow formula in step 1, the corresponding node related branch active power and reactive power are calculated, and the Gaussian noise is added on the basis of the calculated branch active and reactive power and the corresponding node voltage amplitude to simulate the SCADA measurement value as the input of the deep learning model, and the expected output of the offline training of the deep learning model is the node active injection power and reactive injection power. Through training samples and test samples, the parameters of the deep learning model are continuously adjusted until the accuracy meets the requirements;

[0122] (2.2) Online calculation of deep learning model

[0123] According to real-time SCADA measurements, including node voltage amplitude measurements and branch power measurements, they are input into the deep learning model which has been trained, and the output is the node active power and node reactive power at the current time, which is used as the node injection power pseudo measurement.

[0124] Further, step 3 reads the real-time measurements of node voltage amplitude and branch power, which are collected by SCADA measurement devices; the read real-time measurements are input into the trained deep learning model to obtain the node active power and node reactive power at the current time, which are used as the node injection power pseudo measurement.

[0125] Further, the linearized weighted least absolute value estimation model of the alternating current system and the linearized weighted least absolute value estimation model of the direct current system in step 4 are as follows:

[0126] For the AC-DC distribution network, the converter naturally divides into multiple AC and DC systems. For the estimation model of the kth AC region, it is expressed as follows:

[0127]

[0128] s.t.z k -h(x k )=e k

[0129] P AC,ci =P VSC,k ,Q AC,ci =Q VSC,k

[0130] P DC,jc -P VSC,loss =P VSC,k'

[0131] In the formula, J() represents the optimization objective function, x k represents the state variable vector of the kth AC region, λ represents a constant coefficient, P VSC,k and P VSC,k’ represent the active power of the converter of the kth AC region and the k'th DC region respectively, Q VSC,k is the reactive power of the converter of the kth AC region, z k represents the measurement vector of the kth AC region, e k represents the measurement residual vector of the kth AC region.

[0132] The linearized expression of the nonlinear power flow equation of the AC system branch power in step 1 is as follows:

[0133]

[0134] wherein U i and U i’ are squares of voltage magnitudes of the ith AC node and the ith' AC node, respectively, R ii’ and X ii’ are resistance and reactance values of branches connected to the ith AC node and the ith' AC node;

[0135] Linearize the nonlinear power flow equation of the AC system in step 1 to obtain the linearized measurement equation:

[0136]

[0137] wherein represents a vector of node voltage magnitude phasors of the AC system, and H is a constant Jacobian matrix;

[0138] The linearized model of the DC system is:

[0139] P DC,jj' = (1-ΔV j )(1-ΔV j' )Y jj'

[0140] ≈ (1-ΔV j -ΔV j' )Y jj'

[0141] wherein ΔV j and ΔV j’ are differences of voltage magnitudes of the jth DC node and the j' th DC node relative to 1, i.e., V j = 1-ΔV j , V j’ = 1-ΔV j’ ;

[0142] For the kth AC region, the linear weighted least absolute value estimation model is:

[0143]

[0144] s.t.u k -l k = z k -H k x k,AC u k,i , l k,i ≥ 0

[0145] a k -b k = P VSC,k -P VSC,k' a k , b k ≥ 0

[0146] P AC,ci = P VSC,k Q AC,ci = Q VSC,k

[0147] P DC,jc - P VSC,loss = P VSC,k' k' ∈ D k

[0148] where D k represents the set of DC regions connected to the kth AC region, J k represents the optimization objective function of the kth AC region, m k represents the number of measurements in the kth AC region, which is the sum of the number of real-time measurements, the number of pseudo measurements and the number of zero injection constraints in the kth AC region, w k,i represents the weight of the ith measurement in the kth AC region, u k,i - l k,i represents the ith measurement residual of the kth AC region, u k - l k represents the measurement residual vector of the kth AC region, where u k,i and l k,i are non-negative numbers, a k - b k represents the boundary information imbalance of the kth AC region, where a k and b k are non-negative numbers, H k is the constant Jacobian matrix of the kth AC region, and x k,AC is the state estimation vector of the kth AC region.

[0149] For the k'th DC region, the linear weighted least absolute value estimation model is:

[0150]

[0151] s.t. u k' - l k' = z k' - H k' x k',DC u k',j , l k',j ≥ 0

[0152] a k' - b k' = P VSC,k - P VSC,k' a k' , b k' ≥ 0

[0153] P AC,ci = P VSC,k Q AC,ci = Q VSC,k

[0154] P DC,jc = P VSC,loss = P VSC,k' k'∈D k

[0155] In the formula, J k’ represents the optimization objective function of the k'th DC area, m k’ represents the number of real-time measurements in the k'th DC area, the number of pseudo-measurements and the number of zero-injection constraints, w k’,j represents the weight of the jth measurement in the k'th DC area, u k’,j -l k’,j represents the jth measurement residual in the k'th DC area, u k’ -l k’ represents the measurement residual vector of the k'th DC area, wherein u k’,j and l k’,j are non-negative numbers, a k’ -b k’ represents the boundary information imbalance of the k'th DC area, wherein a k’ and b k’ are non-negative numbers, H k’ is the constant Jacobian matrix of the k'th DC area, x k’,DC is the state estimation vector of the k'th DC area, and z k’ is the measurement vector of the k'th DC area.

[0156] Further, the boundary information calculation method of step 5 is as follows:

[0157]

[0158] P AC,ci = P DC,jc = P VSC,loss

[0159] In the formula, d1, d2, d3 represent the constant coefficients of the converter loss, V c and I c represent the voltage and current amplitudes of the AC side connection point of the converter.

[0160] Further, the criterion that the boundary information difference is within the allowed error range is as follows:

[0161] P VSC,k = P VSC,k' ≤τor l<L max

[0162] where τ is a preset convergence threshold, l represents the current iteration number, L max is the maximum iteration number between areas.

[0163] Example analysis

[0164] 1) Example description

[0165] The test system of the present application is a simple 33-node AC / DC distribution network, and the system structure is shown in Figure 3 The nodes 17, 22 and 32 in the DC distribution network are connected to distributed photovoltaic, the node 24 in the AC distribution network is connected to a wind turbine, and the nodes 9 and 29 are connected to diesel generators. The measurement configuration of the AC / DC distribution network is as follows: 1) the SCADA measurement configuration is at the main transformer and the converter node, four AC lines and all DC lines; 2) the smart meter is configured at the load node. Among them, the uncertainty level of SCADA voltage measurement is 1%, the uncertainty level of SCADA branch power measurement is 2%, and the uncertainty level of smart meter data is 2%, mainly the node injection power. The load and power generation information is taken from a real distribution network in Jiangsu from January 1, 2013 to April 1, 2014.

[0166] 2) Deep learning model of node injection power

[0167] Firstly, based on the historical smart meter data, the probability distribution of the node injection power is fitted, as shown in Figure 4 , which are the active power probability distributions of nodes 5 and 9, respectively. Through analysis, it can be found that the probability distribution of the node injection power can be fitted by using a 2-component Gaussian mixture model. Figure 5 The node injection power error diagram output by the deep learning model can be seen that the active and reactive power errors of all nodes are within 0.006 p.u. and 0.0025 p.u., respectively.

[0168] 3) Comparison of the present application algorithm with other methods

[0169] The comparison algorithms mainly include centralized WLS (Centralized WLS, CWLS) and decentralized WLS (Decentralized WLS, DWLS). At each time section, the two comparison algorithms and the decentralized robust state estimation (Decentralized Robust State Estimation, DRSE) of the AC / DC distribution network based on smart meter data proposed in the present application are used. The average absolute error (Average Absolute Error, AAE) and the maximum absolute error (Maximum Absolute Error, MAE) are used to measure the estimation accuracy:

[0170]

[0171]

[0172] where n is the number of state variables; x i represent the true value of power flow calculation.

[0173] The test results are shown in Table 1. Figure 6 As shown in Table 1, it is obvious that the deep learning model can significantly reduce the state estimation error of the alternating current node among the three state estimation methods, and due to the linearization process, the estimation accuracy of the distributed robust state estimation method proposed in the application decreases slightly. This is due to the linearization of the power flow measurement equation ignoring the phase angle difference at both ends of the line, but the estimation accuracy is still within an acceptable range. The estimation error of the direct current node has almost no change under different pseudo-measurement models, because the pseudo-measurement model is mainly applied to the alternating current load node, which significantly improves the measurement redundancy of the alternating current power grid.

[0174] 4) Calculation efficiency

[0175] The distribution network has a large number of nodes and is relatively dispersed, so the calculation efficiency and time are one of the main measurement standards to ensure that the algorithm is applied to practical engineering. It should be noted that the DRSE proposed in the application uses parallel computing for distributed calculation of the alternating current and direct current system, so when calculating the calculation time in one iteration, only the maximum calculation time of the alternating current or direct current system is counted. The calculation time of the two distributed estimation methods is shown in Table 1, and it can be seen that as the number of system nodes increases, the calculation time of the DRSE proposed in the application is significantly less than that of the DWLS, saving about 40% of the time.

[0176] Table 1 Calculation time of different distributed estimation methods

[0177]

Claims

1. A distributed robust state estimation method for AC / DC distribution networks based on smart meter data, characterized in that: The following steps are involved: Step 1: Establish a three-phase model of the AC / DC distribution network based on parameter information of the AC / DC distribution network, wherein the parameter information includes resistance and reactance of the three-phase branches of the AC distribution network, resistance of the three-phase branches of the DC distribution network, and equivalent resistance and reactance of the voltage source converter equivalent model; Step 2: Establish a deep learning model, use historical smart meter data and power flow calculation to generate sample data, and perform offline training. The node voltage amplitude data and branch power data in the sample data are the inputs of the deep learning model training, and the node active injection power and node reactive injection power are the outputs of the deep learning model training; Step 3: Read the real-time measurements of node voltage amplitude and branch power, and input the real-time measurements into the trained deep learning model to obtain pseudo-measurements of node active injection power and node reactive injection power; Step 4: Establish a linearized weighted minimum absolute value estimation model for the AC system and a weighted minimum absolute value estimation model for the DC system; Step 5: Introduce the real-time SCADA measurement, node injection power pseudo-measurement, zero injection constraint and boundary information into the linearized weighted minimum absolute value estimation model of the AC system and the weighted minimum absolute value estimation model of the DC system established in step 4, perform robust estimation on the AC and DC systems respectively, and calculate the state estimation values ​​of the AC and DC systems. The SCADA measurement includes the node voltage amplitude and branch power measurement. The node injection power pseudo-measurement is the node active injection power and node reactive injection power generated by the deep learning model in step 3. The zero injection constraint refers to the active injection and reactive injection of the connecting node in the power grid is zero. The boundary information refers to the loss power and active and reactive power of the voltage source converter at the connection boundary of the AC network and the DC network; Step 6: Calculate the boundary information of the AC and DC systems based on the state estimate, exchange the boundary information of the AC and DC systems, and determine whether the difference in boundary information calculated in different areas is within the allowable error range. If not, update the boundary information and repeat steps 5 and 6; if so, save and output the state estimate of the AC and DC systems.

2. A distributed robust state estimation method for AC / DC distribution networks based on smart meter data according to claim 1, characterized in that: In step 1, a three-phase model of the AC / DC distribution network is established based on the parameter information of the AC / DC distribution network. The parameter information includes the resistance and reactance of the three-phase branches of the AC distribution network, the resistance of the three-phase branches of the DC distribution network, and the equivalent resistance and reactance of the voltage source converter equivalent model. The constructed three-phase model of the AC / DC distribution network includes state variables, measurement equations, and a converter equivalent model, as follows: (1.1) State variables The state variables x of the AC / DC distribution network include the voltage amplitude and phase angle of the AC node and the voltage amplitude of the DC node, as shown below: Where x AC,i represents the state variable of the ith communication node, x DC,j represents the state variable of the jth DC node, N AC and N DC A collection of nodes representing the AC system and the DC system; (1.2) Measurement equations and converter equivalent models The AC and DC current measurement equations can be expressed as follows: zh(x)=e Where z represents the measurement vector, x represents the state variable vector, h() represents the AC or DC power flow equation, and e represents the measurement residual vector; For AC systems, the measurements include node voltage amplitude measurement, node active injection power measurement, node reactive injection power measurement, branch active power measurement, and branch reactive power measurement. The power flow equation is as follows: i ii' =θ i -θ i' {i,i'}∈N AC Where, P AC,ii’ and Q AC,ii’ Represent the active and reactive powers of the branches connected to the i-th AC node and the i'th AC node, respectively. V i and V i’ Represent the voltage amplitude of the i-th AC node and the i'th AC node, θ ii’ Represents the phase angle difference between the branches connected to the i-th AC node and the i'th AC node, θ i and θ i’ Represent the phase angles of the ith AC node and the i'th AC node, P AC,i and Q AC,i represent the active injection power and reactive injection power of the i-th AC node, respectively. and represent the branch active power measurement error and branch reactive power measurement error of the branch connected to the i-th AC node and the i'th AC node, respectively. and They represent the measurement error of active power injection and reactive power injection of the i-th AC node, G ii’ and B ii’ Represent the real and imaginary parts of the admittance matrix of the branch connected to the ith AC node and the ith' AC node, respectively. The voltage amplitude V in the AC system power flow equation is i and V i’ , voltage phase angle θ i and θ i’ The part corresponding to the AC system in the state variable vector x; For DC systems, measurements include node voltage amplitude measurement, node active injection power measurement, and branch active power measurement. The power flow equation is as follows: Where V j and V j’ Represent the voltage amplitudes of the jth DC node and the j'th DC node, P DC,j represents the active injection power of the jth DC node, P DC,jj’ represents the branch active power of the branch connected to the jth DC node and the j'th DC node, Y jj’ represents the branch admittance of the branch connecting the jth DC node and the j'th DC node, represents the measurement error of the active injected power at the jth DC node, represents the branch active power measurement error of the branch connected to the jth DC node and the j'th DC node, and the voltage amplitude V in the DC system power flow equation. j and V j’ The part corresponding to the DC system in the state variable vector x; For the voltage source converter at the boundary of the AC / DC system, an equivalent model of the converter is constructed: Assume that a converter in the AC / DC distribution network is connected to AC node i. The converter is equivalent to a model connected to an equivalent AC branch and an ideal converter. The two endpoints of the equivalent AC branch are the i-th AC node and the equivalent c-th AC node, respectively. The measurement equation of the converter is as follows: P AC,ci -P VSC =0 Q AC,ci -Q VSC =0 P VSC +P VSC,loss =P DC,jc Where, P VSC Represents the converter active power, Q VSC Represents the reactive power of the converter, P AC,ci and Q AC,ci represent the active power and reactive power flowing from the cth AC node to the ith AC node, P VSC,loss Represents the active power loss on the converter, P DC,jc Represents the active power flowing from the jth DC node to the cth AC node.

3. The method for distributed robust state estimation of AC / DC distribution networks based on smart meter data according to claim 2, characterized in that: The deep learning model described in step 2 is established. The model training and application process is as follows: (2.1) Offline training of deep learning models Based on historical smart meter data, the distribution of node active and reactive injection power is learned. The active and reactive injection powers of the nodes are sampled using Monte Carlo. The voltage amplitude and phase angle of all nodes in the entire network are calculated using the power flow equation formula in step 1. The voltage amplitude and phase angle of all nodes in the entire network are used to calculate the corresponding node-related branch active power and reactive power according to the node location of the SCADA measurement point using the power flow formula in step 1. Gaussian noise is added to the calculated branch active and reactive power and the voltage amplitude of the corresponding node to simulate the SCADA measurement value. This is used as the input of the deep learning model. The expected output of the offline training of the deep learning model is the node active and reactive injection power. The parameters of the deep learning model are continuously adjusted through training samples and test samples until the accuracy meets the requirements. (2.2) Online calculation of deep learning models Real-time SCADA measurements, including node voltage amplitude and branch power measurements, are input into a trained deep learning model. The output is the node active power and node reactive power at the current moment, which are used as pseudo-measurements of node injected power.

4. A distributed robust state estimation method for AC / DC distribution networks based on smart meter data according to claim 3, characterized in that: The real-time measurement of the node voltage amplitude and branch power described in step 3 is collected by the SCADA measurement device; the read real-time measurement is input into the trained deep learning model to obtain the node active power and node reactive power at the current moment, which are used as the node injection power pseudo-measurement.

5. The method for distributed robust state estimation of AC / DC distribution networks based on smart meter data according to claim 4, characterized in that: The linearized weighted minimum absolute value estimation model for the AC system and the linearized weighted minimum absolute value estimation model for the DC system described in step 4 are specifically as follows: The AC / DC distribution network is naturally divided into multiple AC and DC systems according to the converters. The estimation model for the kth AC area is expressed as follows: s.t.z k -h(x k )=e k P AC,ci =P VSC,k ,Q AC,ci =Q VSC,k P DC,jc -P VSC,loss =P VSC,k' Where J() represents the optimization objective function, x k represents the state variable vector of the kth AC region, λ represents the constant coefficient, P VSC,k and P VSC,k’ represents the converter active power of the kth AC region and the k'th DC region, Q VSC,k is the reactive power of the converter in the kth AC region, z k represents the measurement vector of the kth AC region, e k Represents the measurement residual vector of the kth AC region; The linearized expression of the nonlinear power flow equation of the AC system branch power in step 1 is as follows: Where U i and U i’ are the squares of the voltage amplitudes of the ith AC node and the i'th AC node, respectively, and R ii’ and X ii’ are the resistance and reactance of the branch connecting the i-th AC node and the i'th AC node; Linearize the nonlinear power flow equation of the AC system in step 1 to obtain the linearized measurement equation: Where, represents the square vector of the node voltage amplitude of the AC system, and H is the constant Jacobian matrix; The linearized model of the DC system is: P DC,jj' =(1-ΔV j )(1-ΔV j' )Y jj' ≈(1-ΔV j -ΔV j' )Y jj' Where ΔV j and ΔV j’ are the differences between the voltage amplitudes of the jth DC node and the j'th DC node relative to 1, that is, V j =1-ΔV j , V j’ =1-ΔV j’ ; For the kth communication area, its linear weighted minimum absolute value estimation model is: s.t.u k -l k =z k -H k x k,AC u k,i ,l k,i ≥0 a k -b k =P VSC,k -P VSC,k' a k ,b k ≥0 P AC,ci =P VSC,k ,Q AC,ci =Q VSC,k P DC,jc -P VSC,loss =P VSC,k' k'∈D k Where D k represents the set of DC regions connected to the kth AC region, J k represents the optimization objective function of the kth communication area, m k The number of measurements in the kth AC region is the sum of the number of real-time measurements, the number of pseudo-measurements, and the number of zero injection constraints in the kth AC region. k,i represents the weight of the ith measurement in the kth communication area, u k,i –l k,i represents the i-th measurement residual of the k-th AC region, u k –l k Represents the measurement residual vector of the kth AC region, where u k,i and l k,i is a non-negative number, a k –b k represents the information imbalance at the boundary of the kth communication area, where a k and b k is a non-negative number, H k is the constant Jacobian matrix of the kth communication region, x k,AC is the state estimation vector of the kth communication area; For the k'th DC region, its linear weighted minimum absolute value estimation model is: s.t.u k' -l k' =z k' -H k' x k',DC u k',j ,l k',j ≥0 a k' -b k' =P VSC,k -P VSC,k' a k' ,b k' ≥0 P AC,ci =P VSC,k ,Q AC,ci =Q VSC,k P DC,jc -P VSC,loss =P VSC,k' k'∈D k Where, J k’ represents the optimization objective function of the k'th DC region, m k’ represents the number of measurements in the k'th DC region, which is the sum of the number of real-time measurements, the number of pseudo measurements, and the number of zero injection constraints in the k'th DC region. k’,j represents the weight of the jth measurement in the k'th DC region, u k’,j –l k’,j represents the jth measurement residual in the k'th DC region, u k’ –l k’ Represents the measurement residual vector of the k'th DC region, where u k’,j and l k’,j is a non-negative number, a k’ –b k’ represents the information imbalance at the k'th DC region boundary, where a k’ and b k’ is a non-negative number, H k’ is the constant Jacobian matrix of the k'th DC region, x k’,DC is the state estimation vector of the k'th DC region, z k’ is the measurement vector of the k'th DC region.

6. A distributed robust state estimation method for AC / DC distribution networks based on smart meter data according to claim 5, characterized in that: The boundary information calculation method described in step 5 is as follows: P AC,ci =P DC,jc -P VSC,loss Where d1, d2, d3 represent the constant coefficients of converter loss, V c and I c Represents the voltage and current amplitudes at the connection points on the AC side of the converter.

7. A distributed robust state estimation method for AC / DC distribution networks based on smart meter data according to claim 6, characterized in that: The criterion for whether the boundary information difference in step 6 is within the allowable error range is: P VSC,k -P VSC,k' ≤τ or l <L max Where τ is the preset convergence threshold, l represents the current number of iterations, and L max is the maximum number of iterations between regions.

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